Identically Distributed Pairs of Partition Statistics
Combinatorics
2007-05-23 v1
Abstract
We show that many theorems which assert that two kinds of partitions of the same integer are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics and that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can infer this identity of distribution functions.
Cite
@article{arxiv.math/0004180,
title = {Identically Distributed Pairs of Partition Statistics},
author = {Herbert S. Wilf},
journal= {arXiv preprint arXiv:math/0004180},
year = {2007}
}